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| Book/Report | FZJ-2018-03782 |
1992
Forschungszentrum Jülich GmbH Zentralbibliothek Verlag
Jülich
Please use a persistent id in citations: http://hdl.handle.net/2128/19140
Report No.: Juel-2602
Abstract: This work presents a very detailed investigation of the diffusion behavior of lattice gases on disordered lattices, where double occupancy of sites is excluded. The main emphasis is on numerical simulations of diffusion in systems which are difficult to treat analytically. The presence of disorder necessitates an ensemble average over different realizations of the disorder, in addition to the thermal average. Thus, much additional computer time is required to achieve satisfactory statistics. To deal with this problem, an vectorizable algorithm has been developed that is faster than the standard methods by an order of magnitude. This algorithm is applied to the study of collective and tracer diffusion in a two state model. A good agreement between the analytical calculations of the collective diffusion behaviour and the numerical results is obtained. Another application of the algorithm is the examination of the critical behavior of the diffusivity of the lattice gases on percolationlattices at the percolation threshold p$_{c}$. Data on the critical behavior of the mean-square displacement of tagged particles are given at various concentrations of the lattice gas, and an interesting plateau behavior of the critical exponent is found, when it is considered as a function of the inverse root- mean-square displacement. A thorough analysis of our data by Sahimi and Arbabi (J. Stat. Phys. 62 (1991) 453) proved an universal behaviour at p$_{c}$. It is pointed out that two-point correlation functions are very important for non-equilibrium states of lattice gases. A simple factorization ansatz is not valid. This is shown by analytical calculations on a linear chain with constant density gradients and corrobated by numerical simulations. An effective medium theory for the collective diffusion of lattice gases on lattices with disordered site-energy is outlined and two different approximations for a solution are introduced. The main problem is the unknown behavior of the two-point correlation functions, which has not yet been derived analytically. The main portion of the simulational work covers the collective and tracer diffusion on large lattices with randomly distributed traps, and insights in the influence of disorder on the transport behavior are obtained. For the first time a wide range of article concentrations as well as trap concentrations and trap depths have been investigated systematically. In higher dimensions two different regimes of the behaviour of the diffusion coefficient have been detected. The simulations show that, for concentrations above the percolation threshold of free sites, the traps are saturated at first with increasing particle concentrations followed by a regime of free diffusion of the additional particles through the lattice. For trap concentrations such that the concentration of free sites is below p$_{c}$ no dependence on the diffusion coefficient from the particle concentration is visible. Therefore, the diffusionis controlled by the dynamics of trapping and releasing on the traps, in the same manner as for single particles. Similar results could be seen for the tracer diffusion.On linear chains, the behaviour of the diffusion coefficient is comparable with the case of absence of percolation at all trap concentrations. This is also observed in the case of tracer diffusion on chains.
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